Publication Date

1-1-2026

Document Type

Article

Publication Title

Journal for Geometry and Graphics

Volume

30

Issue

1

First Page

45

Last Page

59

Abstract

We apply Heron's formula to obtain a generalized Ptolemy's theorem, to prove Euler's formula for the volume of a tetrahedron, and to prove Klain's theorem on reversible tetrahedra. After that, we prove triangle inequalities derived from a tetrahedron, find an inequality on the circumradius of a tetrahedron, find a volume expression of an isosceles tetrahedron, and give a condition for four points in the space to be co-planar.

Keywords

Bang's theorem, circumradius of a tetrahedron, Euler's formula, Heron's formula, isosceles tetrahedron, Klain's theorem, parallelogram law, reversible tetrahedron

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

Department

Mathematics and Statistics

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